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On The Cyclicity And Synthesis Of Diagonal Operators On The Space Of Functions Analytic On A Disk

Deters, Ian Nathaniel
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1236617862

Abstract Details

2009, Doctor of Philosophy (Ph.D.), Bowling Green State University, Mathematics.
A diagonal operator on the space of functions holomorphic on a disk of finite radius is a continuous linear operator having the monomials as eigenvectors. In this dissertation, necessary and sufficient conditions are given for a diagonal operator to be cyclic. Necessary and sufficient conditions are also given for a cyclic diagonal operator to admit spectral synthesis, that is, to have as closed invariant subspaces only the closed linear span of sets of eigenvectors. In particular, it is shown that a cyclic diagonal operator admits synthesis if and only if one vector, not depending on the operator, is cyclic. It is also shown that this is equivalent to existence of sequences of polynomials which seperate and have minimum growth on the eigenvalues of the operator.
Steven Seubert, Ph.D. (Advisor)
Neal Carothers, Ph.D. (Committee Member)
Sachi Sakthivel, Ph.D. (Committee Member)
J. Gordan Wade, Ph.D. (Committee Member)
65 p.
Mathematics
cyclic vectors; spectral synthesis; invariant subspaces; diagonal operators

Recommended Citations

Citations

  • Deters, I. N. (2009). On The Cyclicity And Synthesis Of Diagonal Operators On The Space Of Functions Analytic On A Disk [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1236617862

    APA Style (7th edition)

  • Deters, Ian. On The Cyclicity And Synthesis Of Diagonal Operators On The Space Of Functions Analytic On A Disk. 2009. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1236617862.

    MLA Style (8th edition)

  • Deters, Ian. "On The Cyclicity And Synthesis Of Diagonal Operators On The Space Of Functions Analytic On A Disk." Doctoral dissertation, Bowling Green State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1236617862

    Chicago Manual of Style (17th edition)

bgsu1236617862
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© 2009, all rights reserved.
This open access ETD is published by Bowling Green State University and OhioLINK.